We may believe, then, that the pyramid of the ancient empire terminated in a pyramidion. This apex once fixed in place, the workmen charged with the final completion of the edifice worked downwards from one course to another, covering the immense steps which each face displayed five or six thousand years ago and now displays again, with the final casing which protected them for so many centuries. Even Herodotus saw that this must have been the method of completion.[217] Any other way of proceeding would have been too dangerous after the slope of the sides had been made smooth and continuous by the completion of the casing of polished granite. Workmen could only have kept their footing upon such a surface, with its 51 or 52 degrees of elevation, by means of a complicated arrangement of ropes and ladders. And again, points of resistance could not have been obtained for the elevation of the materials to ever increasing heights without cutting or leaving holes in the casing, which would afterwards have to be filled up. These difficulties would have unnecessarily complicated an operation which was a simple matter when begun from the top. The masons could then make use of the steps for their own locomotion, and when the stones were too large to be lifted from hand to hand, nothing could be easier than to fix windlasses by which the largest blocks could be raised with facility. [217] Ἐξεποιήθη δ' ὦν τὰ ἀνώτατα αὐτῆς πρῶτα, μετὰ δὲ τὰ ἑπόμενα τούτων ἐξεποίευν ... (ii. 125). As the workmen approached the base they left above them an ever increasing extent of polished surface, sloping at such an angle that no foot could rest upon it, and forming the only safeguard against the degradation of the pyramid by removing its copestone or its violation by breaking into the passages which led to the mummy-chamber. The casing gave to the pyramid those continuous lines which were necessary to make its beauty complete, and, if the materials employed were varied in the way suggested, it furnished colour effects which had their beauty also. But, above all, it was a protection, a defensive armour. So long as the pyramid preserved its cuirass intact, it was difficult for those who meditated violence to know where to begin their attack. But this obstacle once pierced it was comparatively easy to learn all the secrets of the building. The inner mass was much less carefully built than the casing; the joints were comparatively open, and the stones were soft and easily cut. Hence we see that some pyramids, especially those which were built of bricks, have been reduced by the action of time into heaps of _débris_, in which the pyramidal form is hardly to be recognised.